The approximate value of 5.1 million x 2.2 thousand is? use scientific notation

(x,-4) and (2,8): m = -3 find the missing value. it is in slope formula.

Snezhnost [94]

Answer:

The value of x = 6

Step-by-step explanation:

Given

The point (x,-4)

The point (2,8)

To determine

m = -3

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

here:

(x₁, y₁) = (x, -4)

(x₂, y₂) = (2, 8)

m = -3

so substitute (x₁, y₁) = (x, -4) , (x₂, y₂) = (2, 8) and m = -3

m = [y₂ - y₁] / [x₂ - x₁]

-3 = [8 - (-4)] / [2 - x]

-3 = [12] / [2-x]

-3 (2-x) = 12

-6+3x = 12

3x = 12+6

3x = 18

divide both sides by 3

3x/3 = 18/3

x = 6

Therefore, the value of x = 6

7 0

3 years ago

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

Angle D and Angle F are supplementary. The measure of Angle D is (3x + 5), and the measure of angle F is (2x). What is the measu

olga55 [171]

Step-by-step explanation:

Two angles are called suplementary when their measures add to 180 degrees.

D+F= 180

3x+5+2x= 180

5x+5=180

5x= 175

x= 35°

angle D = 3x+5= 3(35)+5= <u>110°</u>

5 0

2 years ago

Please Help Me!!!!!! I have a big test tomorrow!!!!!!!! I will give 30 points!!!!!!!!! The expression represents the number of m

il63 [147K]

Answer:

For this expression I guessed I would use subtraction because when you subtract Kimiko's miles to Celeste's miles you could see how much faster Kimiko was than Celeste.

Step-by-step explanation:

4 0

2 years ago

Someone please help me out with these questions . I don’t get them at all.

iVinArrow [24]

Answer:

a)similar; b)similar; c)similar; d)NOT similar

Step-by-step explanation:

>In general if

all corresponding angels are ≅, and

all corresponding sides are in proportion

then the Δs are similar

>we have 3 similarity theorems AA, SSS, and SAS

a)

we can use that sum of angles in a triangle is 180 to find the missing angles

180-96-32 = 52

so in the smaller triangle the angles are 96°-52°-32°

in the larger triangle the angles given are 52°-32°

Since there are 2 corresponding angles congruent, AA theorem of similarity says that the 2 triangles are similar. The transformations were that the big triangle was shrunk and rotated

b)

here we are given a pair of congruent angles and we need to check if the sides are in proportion, is 14/44.8 equal to 20/64?

14/44.8 =.3125 is equal to 20/64=.3125

since we have two corresponding sides in proportion and the angles in between them congruent the SAS theorem says that the 2 triangles are similar. The transformation was that the small triangle was dilated.

c)

because we are given the 2 angles are congruent we can conclude that the lines NH and SL are parallel. NH║SL let us conclude that ∡H and ∡ L are congruent because 2 parallel lines cut by a transversal (ML in our case) form congruent angles. So ΔMNH is similar to ΔMSL because of AA theorem of similarity (one pair of A was given congruent, one other pair of A we concluded was congruent)

d)

here we have to check if all the sides are in proportion to see if SSS theorem of similarity applies here

18/90 = .2

44/202.4≈.22

58.5/211.2≈.28

.2≠ .22 ≠ .28

since the sides are not in proportion the 2 triangles are NOT similar.

4 0

3 years ago